Weighted Mean Calculator
Calculate the weighted mean of a dataset using values and their corresponding weights. Enter or paste your data, review each weighted contribution, and follow the calculation step by step.
See the weighted mean
Enter your values, or try an example.
Your results and calculation will appear here.
Show weighted calculation table
Weight share = w / total weight. Mean contribution = (value × weight) / total weight. This table describes the entered known rows.
| Item | Value | Weight | Value × Weight | Weight share | Mean contribution |
|---|
Show calculation
How to use this calculator
- Enter each data value with its corresponding weight, or paste value-weight pairs from a spreadsheet.
- Add or remove rows as needed. Weights can represent frequencies, percentages, or other nonnegative relative weights.
- Select Calculate to find the weighted mean, total weight, and weighted sum.
- Open the calculation table or calculation steps to see how each value contributes to the result.
Worked example: weighted mean from a data table
This example uses sample values, not your current inputs.
Suppose three measurements have values 10, 20, and 30, with corresponding weights 2, 3, and 5. Find their weighted mean.
| Value | Weight | Weighted product |
|---|---|---|
| 10 | 2 | 20 |
| 20 | 3 | 60 |
| 30 | 5 | 150 |
- Weighted mean
- 23Weighted sum: 230 · Total weight: 10
The weighted mean is 23. The value 30 has the largest weight, so it contributes more to the result than either 10 or 20.
Example calculation
- Multiply each value by its weight: 10 × 2 = 20; 20 × 3 = 60; 30 × 5 = 150.
- Add the weighted products: 20 + 60 + 150 = 230.
- Add the weights: 2 + 3 + 5 = 10.
- Divide: 230 / 10 = 23.
Formula & assumptions
x̄w = Σᵢ₌₁ⁿ wᵢxᵢ / Σᵢ₌₁ⁿ wᵢ
- xᵢ
- Individual data value
- wᵢ
- Weight assigned to that value
- n
- Number of value–weight pairs
- Σwᵢxᵢ
- Sum of the weighted products
- Σwᵢ
- Total weight, which must be greater than zero
Assumptions
- Each value must have a corresponding weight.
- Weights must be nonnegative, and at least one weight must be positive.
- Weights may be counts, proportions, percentages, or other consistent relative weights.
- Weights do not have to add up to 1 or 100; the calculation normalizes them automatically.
- Data values may be negative. A zero weight gives a row no influence on the result.
- The calculator computes a weighted arithmetic mean, not the statistical uncertainty of that mean.
Sources
Reviewed: October 2026
Weighted Mean vs. Arithmetic Mean
An arithmetic mean gives every observation equal weight. A weighted mean allows some observations to count more than others. If every value has the same positive weight, the two calculations give the same result.
For values 10, 20, and 30, the arithmetic mean is 20. With weights 2, 3, and 5, the weighted mean is 23. The results differ because the larger values receive more weight.
Understanding weights
Weights describe how strongly each value contributes to the result. For a frequency table, a weight can be the number of times a value occurs. For a course grade, it can represent the relative share of an assignment or examination. In scientific data, weights may reflect a specified relative importance, but the choice of weights must be justified by the problem.
Using weights of 20, 30, and 50 gives the same weighted mean as using 0.20, 0.30, and 0.50 for the same values.
Weighted mean in Excel
If values are in cells A2:A4 and their corresponding weights are in B2:B4, the weighted mean can be calculated in Excel with:
=SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4)SUMPRODUCT multiplies the matching values and weights and adds the products. SUM adds the weights. The denominator must not be zero.
Common questions
What is a weighted mean?
A weighted mean summarizes values while allowing them to have different levels of influence. For example, a final exam worth 50% of a course grade has more influence than an assignment worth 10%. The weights describe that relative influence.
How do you calculate the weighted mean?
Multiply each value by its corresponding weight, add the weighted products, and divide by the sum of the weights. For values 10, 20, and 30 with weights 2, 3, and 5, the result is (10×2 + 20×3 + 30×5) / (2+3+5) = 23.
Is weighted mean the same as weighted average?
Yes. In most introductory mathematics and statistics problems, weighted mean and weighted average refer to the same calculation: the sum of weighted values divided by the sum of the weights.
Do weights have to add up to 100%?
No. The calculator divides by the actual sum of the weights, so weights such as 2, 3, and 5 work just as well as 20, 30, and 50. However, if your weights are intended to describe all parts of a course or another complete percentage breakdown, a total other than 100% may indicate that something is missing.
Can I use frequencies as weights?
Yes. If a value occurs several times, its frequency can be used as its weight. For example, the values 10 and 20 with frequencies 2 and 3 have a weighted mean of (10×2 + 20×3) / 5 = 16. Frequencies represent counts and should be nonnegative integers.
Can the values or weights be negative?
Data values may be negative, but this calculator requires nonnegative weights. A weight of zero is allowed and excludes that row from the weighted result. At least one weight must be positive.
When does the weighted mean equal the arithmetic mean?
If all values have the same positive weight, the weighted mean equals the ordinary arithmetic mean. Unequal weights can produce a different result, although the two means may sometimes coincide for a particular dataset.
Why is my weighted mean different from the regular mean?
The regular mean treats every entered value equally. If your weighted mean is higher, the larger values have received more weight overall; if it is lower, the smaller values have received more weight. Check that each weight is paired with the intended value, especially after copying data.
How can I calculate the weighted mean in Excel?
Put the values in one column and their corresponding weights in another. For values in A2:A4 and weights in B2:B4, use =SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4). Keep both ranges the same size and make sure the sum of the weights is greater than zero.
Can I find a missing value needed for a target weighted mean?
Yes. Use the optional target-value calculation to find one additional value with a known weight that will produce your chosen weighted mean. The calculator uses the existing weighted sum and total weight, then verifies the result after adding the new item. Enter only the known rows in the main table; this mode does not fill an empty cell in an existing row.
Use these tools for mathematical information, not as a substitute for checking assumptions. Read our methodology or disclaimer.